1. neural quantum state of the long-range antiferromagnetic ising chain

Dong-Hee Kim

Gwangju Institute of Science and Technology, Korea

8 February 2022 Tue 5 pm

                                      IBS Center for Theoretical Physics of Complex Systems (PCS), Administrative Office (B349), Theory Wing, 3rd floor

                                      Expo-ro 55, Yuseong-gu, Daejeon, South Korea, 34126 Tel: +82-42-878-8633                     

We study a quantum phase transition in a quantum Ising chain with power-law-decaying antiferromagnetic interactions using a variational Monte-Carlo method with the neural-network quantum state (NQS) ansatz based on the restricted Boltzmann machine. We mainly focus on the regime of the decay exponent less than two, where the characterization of the critical behavior is not fully agreed between previous works. Our finite-size-scaling analysis in systems with the periodic boundary condition shows that the critical exponents of magnetization and susceptibilities agree with the Ising universality class at all values of the decay exponent examined. Our second Renyi entanglement entropy calculation also supports the central charge 1/2 expected in the Ising class. However, away from the critical point, it turns out that the correlation function decays algebraically due to the long-range nature of the interaction, and a weak violation of the area law is also observed at small values of the decay exponent.